San Francisco — Gap Inc. has appointed Nancy Green as the president and CEO of Old Navy, the company’s largest brand. Green will report to Sonia Syngal, CEO of Gap Inc., and will serve on the company’s senior leadership team. Green has served as interim head of Old Navy since March and was previously president and chief creative officer of the brand. “Nancy is a visionary leader who brings deep customer empathy to her role every day. She has led the brand through one of the most challenging periods in …